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/* Compute cubic root of double value.
Copyright (C) 1997-2020 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include <math.h>
#include <libm-alias-ldouble.h>
#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
/* We don't use long double values here since U need not be computed
with full precision. */
static const double factor[5] =
{
1.0 / SQR_CBRT2,
1.0 / CBRT2,
1.0,
CBRT2,
SQR_CBRT2
};
static const long double third = 0.3333333333333333333333333L;
long double
__cbrtl (long double x)
{
long double xm, u;
int xe;
/* Reduce X. XM now is an range 1.0 to 0.5. */
xm = __frexpl (fabsl (x), &xe);
/* If X is not finite or is null return it (with raising exceptions
if necessary.
Note: *Our* version of `frexp' sets XE to zero if the argument is
Inf or NaN. This is not portable but faster. */
if (xe == 0 && fpclassify (x) <= FP_ZERO)
return x + x;
u = (((-1.34661104733595206551E-1 * xm
+ 5.46646013663955245034E-1) * xm
- 9.54382247715094465250E-1) * xm
+ 1.13999833547172932737E0) * xm
+ 4.02389795645447521269E-1;
u *= factor[2 + xe % 3];
u = __ldexpl (x > 0.0 ? u : -u, xe / 3);
u -= (u - (x / (u * u))) * third;
u -= (u - (x / (u * u))) * third;
return u;
}
libm_alias_ldouble (__cbrt, cbrt)
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